Assuming that your game exists in a single Unity project, the bare minimum that you'll need from them is the project folder that the project belongs to. This is enough to build and run the project and you'll have access to all of the code and assets used in the project.
Anything beyond that is somewhat optional, but it may be a good idea to ask for their acquisition, assuming they were used by the previous developers.
- Asset Project Files: Things such as Photoshop PSDs, Maya Projects, etc. Anything that may increase productivity and make it easier to make changes to existing game assets.
- Game Design Documents: This is assuming that the previous developers had creative responsibilities on the game, but if so, it may be a good idea to ask for any documents they've used so that you have an appropriate understanding of what they were going on.
- Project Management: Anything from a to-do-list text file to a Trello or Slack. Anything that was used by the previous developers, and may alert you of existing bugs or unfinished systems in the project, so that you know how to properly continue where they left off.
- Unity Version: If they're not using the latest version of Unity, it would probably be a good idea to know what version they were using, since large projects may contain many breaking changes when ported to a newer version.
- Unity Asset Store Extensions: Most assets that any previous development team used will be included in the Project file, and will work fine, but I can imagine some that used advanced DRM/Authentication systems may pose a problem when launched on a new system. It may be a good idea to ask for a list of third-party assets that the previous developers used, not only so you know what to expect if you encounter problems, but also so you'll have the same tools that they used for development.
You should be able to communicate with the previous developers if you encounter any problems with the transition, or find out that there's something you need that they haven't provided.
